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Show that X^((1)/(2))*X^((1)/(4))*X^((1...

Show that `X^((1)/(2))*X^((1)/(4))*X^((1)/(8))`... Upto `oo = X `

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To show that \( X^{\frac{1}{2}} \cdot X^{\frac{1}{4}} \cdot X^{\frac{1}{8}} \cdots \) up to infinity equals \( X \), we can follow these steps: ### Step 1: Rewrite the expression We start with the left-hand side of the equation: \[ X^{\frac{1}{2}} \cdot X^{\frac{1}{4}} \cdot X^{\frac{1}{8}} \cdots \] Using the property of exponents that states \( a^m \cdot a^n = a^{m+n} \), we can combine the terms: ...
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